Weak-Hamiltonian dynamical systems

A big-isotropic structure $E$ is an isotropic subbundle of $TM\oplus T^*M$, endowed with the metric defined by pairing. The structure $E$ is said to be integrable if the Courant bracket $[\mathcal{X},\mathcal{Y}]\in\Gamma E$, $\forall\mathcal{X},\mathcal{Y}\in\Gamma E$. Then, necessarily, one also has $[\mathcal{X},\mathcal{Z}]\in\Gamma E^\perp$, $\forall\mathcal{Z}\in\Gamma E^\perp$ \cite{V-iso}. A weak-Hamiltonian dynamical system is a vector field $X_H$ such that $(X_H,dH)\in E^\perp$ $(H\in C^\infty(M))$. We obtain the explicit expression of $X_H$ and of the integrability conditions of $E$ under the regularity condition $dim(pr_{T^*M}E)=const.$ We show that the port-controlled, Hamiltonian systems (in particular, constrained mechanics) \cite{{BR},{DS}} may be interpreted as weak-Hamiltonian systems. Finally, we give reduction theorems for weak-Hamiltonian systems and a corresponding corollary for constrained mechanical systems.Comment: 19 pages, minor improvement

Symmetry and reduction in implicit generalized Hamiltonian systems

In this paper the notion of symmetry for implicit generalized Hamiltonian systems will be studied and a reduction theorem, generalizing the 'classical' reduction theorems of symplectic and Poisson-Hamiltonian systems, will be derived. \u

Eine deutsch-französische Beziehungs(kunst)geschichte? Alexander von Humboldt und die Künste zwischen Paris und Berlin

Au milieu du dix-neuvi'eme siècle, Alexander von Humboldt s’était (déjà) investi pendant presque cinquante ans dans les beaux-arts, en France comme en Prusse. Engagé dans les trans ferts artistiques depuis le règne de Napoléon Ier, il fut impliqué dans la circulation d’oeuvres d’art et d’artistes, de même que dans les échanges entre les académies des beaux-arts pari siennes et berlinoises. Jouant sur ses rapports personnels étroits avec les artistes et les adminis trateurs dans les deux capitales, ses actions manifestent également une connaissance détaillée des structures de la vie artistique, qu’il mit au profit des échanges artistiques franco-prussien

Matching in the method of controlled Lagrangians and IDA-passivity based control

This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The $\lambda$-method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u

Reduction of Generalized Complex Structures

We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is proper and free so that $M_G:=M_0/G$ is a smooth manifold. Under what condition does $J$ descend to a generalized complex structure on $M_G$? We describe a sufficient condition for the reduction to hold, which includes the Marsden-Weinstein reduction of symplectic manifolds and the reduction of the complex structures in K\"ahler manifolds as special cases. As an application, we study reduction of generalized K\"ahler manifolds.Comment: 21 pages, definitive versio

Singular reduction of implicit Hamiltonian systems

This paper develops the reduction theory of implicit Hamiltonian systems admitting a symmetry group at a singular value of the momentum map. The results naturally extend those known for (explicit) Hamiltonian systems described by Poisson brackets.Comment: 29 pages, no figures, submitte

Implicit Lagrange-Routh Equations and Dirac Reduction

In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange-Routh equations can be described in the context of dynamical systems associated to Dirac structures, in which we fully utilize a symmetry reduction procedure for implicit Hamiltonian systems with symmetry.Comment: 21 pages, to appear in J. Geom. Phy

Writing information transfers for out-of-hours palliative care : a controlled trial among GPs

Objective: The aim was to evaluate the effect of the implementation of an information handover form regarding patients receiving palliative care. Outcome was the information available for the out-of-hours GP co-operative. Design: We conducted a controlled trial. Setting: All GPs in Amsterdam, The Netherlands. Intervention: The experimental group (N=240) received an information handover form and an invitation for a one-hour training, the control group (N= 186) did not receive a handover form or training. We studied contacts with the GP co-operative concerning patients in palliative care for the presence and quality of information transferred by the patient's own GP. Main outcome measures: Proportion of contacts in which information was available and proportion of adequate information transfer. Results. Overall information was transferred by the GPs in 179 of the 772 first palliative contacts (23.2%). The number of contacts in the experimental group in which information was available increased significantly after intervention from 21% to 30%, compared to a decrease from 23% to 19% in the control group. The training had no additional effect. The content of the transferred information was adequate in 61.5%. There was no significant difference in the quality of the content between the groups. Conclusion: The introduction of a handover form resulted in a moderate increase of information transfers to the GP co-operative. However, the total percentage of contacts in which this information was present remained rather low. GP co-operatives should develop additional policies to improve information transfer. Key points: The out-of-hours period is potentially problematic for the delivery of optimal palliative care, often due to inadequate information transfer. Introduction of a handover form resulted in a moderate increase of transferred information. The percentage of palliative contacts remained low in cases where information was available. Adequate information was transferred in more than half of the cases

The European Budget: Consolidation or Modernisation?

__Abstract__ This chapter first focuses on the unique character of the European budget [section 2]. We then look back on the Dutch position during the negotiations on the Financial Perspectives 2007-2013 [section 3]2. The subsequent sections respectively address the opening position of the European Commission [section 4] and the Dutch position [section 5] in the negotiations on the Multiannual Financial Framework 2014-2020. The Netherlands aims for modernisation of the budget in which case the current rebate on the Dutch contribution to the European Union could be dropped. The chapter ends with some concluding observations cumulating in a plea for compensation on the expenditure side instead of on the revenue side of the budget